Abstract:

Many engineering applications such as infrastructure operation and model predictive control (MPC) involve solving similar optimization problems over and over and over and over again, with slightly varying input parameters. Electric grid optimization, which is influenced by variable renewable energy generation, is a prominent example. In this talk, we consider the problem of using information available through this repeated solution process to directly learn the optimal solution as a function of the input parameters, thus reducing the need of for computation in real time.

To overcome limitations of existing methods, which typically struggle to enforce feasibility constraints or leverage the knowledge available in the mathematical model, we propose a learning framework based on identifying the relevant sets of active constraints. Using the active sets as an intermediate step enables efficient recovery of the optimal solution, inherently accounts for relevant safety constraints and provides more interpretable results. Further, while the number of possible active sets is combinatorial in the system size, the number of practically relevant active sets can be small, which make them simpler objects to learn. To identify the relevant active sets, we propose a streaming algorithm with rigorous probabilistic performance guarantees. The algorithm is demonstrated using the optimal power flow (OPF) with renewable energy production as an example. We establish that the number of active sets is typically small in this problem, and discuss practical interpretations for power system operation.